Gf.tx_zero: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/aes/gf.bend as Gf
Lines 208-211 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/aes/gf.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/aes/gf.bend&start_line=208&end_line=211

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/crypto/aes/poly.bend as P

def tx_zero(+n: Nat, +low: Word(n)) -> {P.times_x(n, low, Word.zero(n)) == Word.zero(n) : Word(n)}:
  %Equal.sym(Bool, P.top(n, Word.zero(n)), False{}, top_zero(n)) : {Word.xor(n, P.wscale(n, _, low), Word.shl(n, Word.zero(n))) == Word.zero(n) : Word(n)}
  %Equal.sym(Word(n), Word.shl(n, Word.zero(n)), Word.zero(n), shl_zero(n)) : {Word.xor(n, Word.zero(n), _) == Word.zero(n) : Word(n)}
  xor_zero_l(n, Word.zero(n))

Uses (13):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.shl
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.xor
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.zero
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/aes/gf.bend&name=shl_zero
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/aes/gf.bend&name=top_zero
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/aes/gf.bend&name=xor_zero_l
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/aes/poly.bend&name=times_x
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/aes/poly.bend&name=top
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/aes/poly.bend&name=wscale